Business Analytics

Decision Trees

Ayush Patel and Jayati Sharma

01 April, 2024

Pre-requisite

You already….

  • Understand linear regression
  • Know data wrangling and data visualization in R

Before we begin

Please install and load the following packages

library(dplyr)
library(tidyverse)
library(ISLR2)
library(tree)



Access lecture slide from the course landing page

About me

I am Ayush.

I am a researcher working at the intersection of data, law, development and economics.

I teach Data Science using R at Gokhale Institute of Politics and Economics

I am a RStudio (Posit) certified tidyverse Instructor.

I am a Researcher at Oxford Poverty and Human development Initiative (OPHI), at the University of Oxford.

Reach me

ayush.ap58@gmail.com

ayush.patel@gipe.ac.in

Learning Objectives

  • Learn about decision trees

What are tree-based methods?

  • Decison trees - utilized for regression and classification problms
  • Decision trees are
    • supervised
    • non-parametric
  • Named so because of their heirarchial, tree-like structure

Tradeoff between flexibility and interpretability

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • For the various methods, the tradeoff between interpretability and flexibility

Source : ISLR : Chapter 2

Download the Data

  • Download the Hitters data from ISLR2 package
ISLR2::Hitters
                   AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun
-Andy Allanson       293   66     1   30  29    14     1    293    66      1
-Alan Ashby          315   81     7   24  38    39    14   3449   835     69
-Alvin Davis         479  130    18   66  72    76     3   1624   457     63
-Andre Dawson        496  141    20   65  78    37    11   5628  1575    225
-Andres Galarraga    321   87    10   39  42    30     2    396   101     12
-Alfredo Griffin     594  169     4   74  51    35    11   4408  1133     19
-Al Newman           185   37     1   23   8    21     2    214    42      1
-Argenis Salazar     298   73     0   24  24     7     3    509   108      0
-Andres Thomas       323   81     6   26  32     8     2    341    86      6
-Andre Thornton      401   92    17   49  66    65    13   5206  1332    253
-Alan Trammell       574  159    21  107  75    59    10   4631  1300     90
-Alex Trevino        202   53     4   31  26    27     9   1876   467     15
-Andy VanSlyke       418  113    13   48  61    47     4   1512   392     41
-Alan Wiggins        239   60     0   30  11    22     6   1941   510      4
-Bill Almon          196   43     7   29  27    30    13   3231   825     36
-Billy Beane         183   39     3   20  15    11     3    201    42      3
-Buddy Bell          568  158    20   89  75    73    15   8068  2273    177
-Buddy Biancalana    190   46     2   24   8    15     5    479   102      5
-Bruce Bochte        407  104     6   57  43    65    12   5233  1478    100
-Bruce Bochy         127   32     8   16  22    14     8    727   180     24
-Barry Bonds         413   92    16   72  48    65     1    413    92     16
-Bobby Bonilla       426  109     3   55  43    62     1    426   109      3
-Bob Boone            22   10     1    4   2     1     6     84    26      2
-Bob Brenly          472  116    16   60  62    74     6   1924   489     67
-Bill Buckner        629  168    18   73 102    40    18   8424  2464    164
-Brett Butler        587  163     4   92  51    70     6   2695   747     17
-Bob Dernier         324   73     4   32  18    22     7   1931   491     13
-Bo Diaz             474  129    10   50  56    40    10   2331   604     61
-Bill Doran          550  152     6   92  37    81     5   2308   633     32
-Brian Downing       513  137    20   90  95    90    14   5201  1382    166
-Bobby Grich         313   84     9   42  30    39    17   6890  1833    224
-Billy Hatcher       419  108     6   55  36    22     3    591   149      8
-Bob Horner          517  141    27   70  87    52     9   3571   994    215
-Brook Jacoby        583  168    17   83  80    56     5   1646   452     44
-Bob Kearney         204   49     6   23  25    12     7   1309   308     27
-Bill Madlock        379  106    10   38  60    30    14   6207  1906    146
-Bobby Meacham       161   36     0   19  10    17     4   1053   244      3
-Bob Melvin          268   60     5   24  25    15     2    350    78      5
-Ben Oglivie         346   98     5   31  53    30    16   5913  1615    235
-Bip Roberts         241   61     1   34  12    14     1    241    61      1
-BillyJo Robidoux    181   41     1   15  21    33     2    232    50      4
-Bill Russell        216   54     0   21  18    15    18   7318  1926     46
-Billy Sample        200   57     6   23  14    14     9   2516   684     46
-Bill Schroeder      217   46     7   32  19     9     4    694   160     32
-Butch Wynegar       194   40     7   19  29    30    11   4183  1069     64
-Chris Bando         254   68     2   28  26    22     6    999   236     21
-Chris Brown         416  132     7   57  49    33     3    932   273     24
-Carmen Castillo     205   57     8   34  32     9     5    756   192     32
-Cecil Cooper        542  140    12   46  75    41    16   7099  2130    235
-Chili Davis         526  146    13   71  70    84     6   2648   715     77
-Carlton Fisk        457  101    14   42  63    22    17   6521  1767    281
-Curt Ford           214   53     2   30  29    23     2    226    59      2
-Cliff Johnson        19    7     0    1   2     1     4     41    13      1
-Carney Lansford     591  168    19   80  72    39     9   4478  1307    113
-Chet Lemon          403  101    12   45  53    39    12   5150  1429    166
-Candy Maldonado     405  102    18   49  85    20     6    950   231     29
-Carmelo Martinez    244   58     9   28  25    35     4   1335   333     49
-Charlie Moore       235   61     3   24  39    21    14   3926  1029     35
-Craig Reynolds      313   78     6   32  41    12    12   3742   968     35
-Cal Ripken          627  177    25   98  81    70     6   3210   927    133
-Cory Snyder         416  113    24   58  69    16     1    416   113     24
-Chris Speier        155   44     6   21  23    15    16   6631  1634     98
-Curt Wilkerson      236   56     0   27  15    11     4   1115   270      1
-Dave Anderson       216   53     1   31  15    22     4    926   210      9
-Doug Baker           24    3     0    1   0     2     3    159    28      0
-Don Baylor          585  139    31   93  94    62    17   7546  1982    315
-Dann Bilardello     191   37     4   12  17    14     4    773   163     16
-Daryl Boston        199   53     5   29  22    21     3    514   120      8
-Darnell Coles       521  142    20   67  86    45     4    815   205     22
-Dave Collins        419  113     1   44  27    44    12   4484  1231     32
-Dave Concepcion     311   81     3   42  30    26    17   8247  2198    100
-Darren Daulton      138   31     8   18  21    38     3    244    53     12
-Doug DeCinces       512  131    26   69  96    52    14   5347  1397    221
-Darrell Evans       507  122    29   78  85    91    18   7761  1947    347
-Dwight Evans        529  137    26   86  97    97    15   6661  1785    291
-Damaso Garcia       424  119     6   57  46    13     9   3651  1046     32
-Dan Gladden         351   97     4   55  29    39     4   1258   353     16
-Danny Heep          195   55     5   24  33    30     8   1313   338     25
-Dave Henderson      388  103    15   59  47    39     6   2174   555     80
-Donnie Hill         339   96     4   37  29    23     4   1064   290     11
-Dave Kingman        561  118    35   70  94    33    16   6677  1575    442
-Davey Lopes         255   70     7   49  35    43    15   6311  1661    154
-Don Mattingly       677  238    31  117 113    53     5   2223   737     93
-Darryl Motley       227   46     7   23  20    12     5   1325   324     44
-Dale Murphy         614  163    29   89  83    75    11   5017  1388    266
-Dwayne Murphy       329   83     9   50  39    56     9   3828   948    145
-Dave Parker         637  174    31   89 116    56    14   6727  2024    247
-Dan Pasqua          280   82    16   44  45    47     2    428   113     25
-Darrell Porter      155   41    12   21  29    22    16   5409  1338    181
-Dick Schofield      458  114    13   67  57    48     4   1350   298     28
-Don Slaught         314   83    13   39  46    16     5   1457   405     28
-Darryl Strawberry   475  123    27   76  93    72     4   1810   471    108
-Dale Sveum          317   78     7   35  35    32     1    317    78      7
-Danny Tartabull     511  138    25   76  96    61     3    592   164     28
-Dickie Thon         278   69     3   24  21    29     8   2079   565     32
-Denny Walling       382  119    13   54  58    36    12   2133   594     41
-Dave Winfield       565  148    24   90 104    77    14   7287  2083    305
-Enos Cabell         277   71     2   27  29    14    15   5952  1647     60
-Eric Davis          415  115    27   97  71    68     3    711   184     45
-Eddie Milner        424  110    15   70  47    36     7   2130   544     38
-Eddie Murray        495  151    17   61  84    78    10   5624  1679    275
-Ernest Riles        524  132     9   69  47    54     2    972   260     14
-Ed Romero           233   49     2   41  23    18     8   1350   336      7
-Ernie Whitt         395  106    16   48  56    35    10   2303   571     86
-Fred Lynn           397  114    23   67  67    53    13   5589  1632    241
-Floyd Rayford       210   37     8   15  19    15     6    994   244     36
-Franklin Stubbs     420   95    23   55  58    37     3    646   139     31
-Frank White         566  154    22   76  84    43    14   6100  1583    131
-George Bell         641  198    31  101 108    41     5   2129   610     92
-Glenn Braggs        215   51     4   19  18    11     1    215    51      4
-George Brett        441  128    16   70  73    80    14   6675  2095    209
-Greg Brock          325   76    16   33  52    37     5   1506   351     71
-Gary Carter         490  125    24   81 105    62    13   6063  1646    271
-Glenn Davis         574  152    31   91 101    64     3    985   260     53
-George Foster       284   64    14   30  42    24    18   7023  1925    348
-Gary Gaetti         596  171    34   91 108    52     6   2862   728    107
-Greg Gagne          472  118    12   63  54    30     4    793   187     14
-George Hendrick     283   77    14   45  47    26    16   6840  1910    259
-Glenn Hubbard       408   94     4   42  36    66     9   3573   866     59
-Garth Iorg          327   85     3   30  44    20     8   2140   568     16
-Gary Matthews       370   96    21   49  46    60    15   6986  1972    231
-Graig Nettles       354   77    16   36  55    41    20   8716  2172    384
-Gary Pettis         539  139     5   93  58    69     5   1469   369     12
-Gary Redus          340   84    11   62  33    47     5   1516   376     42
-Garry Templeton     510  126     2   42  44    35    11   5562  1578     44
-Gorman Thomas       315   59    16   45  36    58    13   4677  1051    268
-Greg Walker         282   78    13   37  51    29     5   1649   453     73
-Gary Ward           380  120     5   54  51    31     8   3118   900     92
-Glenn Wilson        584  158    15   70  84    42     5   2358   636     58
-Harold Baines       570  169    21   72  88    38     7   3754  1077    140
-Hubie Brooks        306  104    14   50  58    25     7   2954   822     55
-Howard Johnson      220   54    10   30  39    31     5   1185   299     40
-Hal McRae           278   70     7   22  37    18    18   7186  2081    190
-Harold Reynolds     445   99     1   46  24    29     4    618   129      1
-Harry Spilman       143   39     5   18  30    15     9    639   151     16
-Herm Winningham     185   40     4   23  11    18     3    524   125      7
-Jesse Barfield      589  170    40  107 108    69     6   2325   634    128
-Juan Beniquez       343  103     6   48  36    40    15   4338  1193     70
-Juan Bonilla        284   69     1   33  18    25     5   1407   361      6
-John Cangelosi      438  103     2   65  32    71     2    440   103      2
-Jose Canseco        600  144    33   85 117    65     2    696   173     38
-Joe Carter          663  200    29  108 121    32     4   1447   404     57
-Jack Clark          232   55     9   34  23    45    12   4405  1213    194
-Jose Cruz           479  133    10   48  72    55    17   7472  2147    153
-Julio Cruz          209   45     0   38  19    42    10   3859   916     23
-Jody Davis          528  132    21   61  74    41     6   2641   671     97
-Jim Dwyer           160   39     8   18  31    22    14   2128   543     56
-Julio Franco        599  183    10   80  74    32     5   2482   715     27
-Jim Gantner         497  136     7   58  38    26    11   3871  1066     40
-Johnny Grubb        210   70    13   32  51    28    15   4040  1130     97
-Jerry Hairston      225   61     5   32  26    26    11   1568   408     25
-Jack Howell         151   41     4   26  21    19     2    288    68      9
-John Kruk           278   86     4   33  38    45     1    278    86      4
-Jeffrey Leonard     341   95     6   48  42    20    10   2964   808     81
-Jim Morrison        537  147    23   58  88    47    10   2744   730     97
-John Moses          399  102     3   56  34    34     5    670   167      4
-Jerry Mumphrey      309   94     5   37  32    26    13   4618  1330     57
-Joe Orsulak         401  100     2   60  19    28     4    876   238      2
-Jorge Orta          336   93     9   35  46    23    15   5779  1610    128
-Jim Presley         616  163    27   83 107    32     3   1437   377     65
-Jamie Quirk         219   47     8   24  26    17    12   1188   286     23
-Johnny Ray          579  174     7   67  78    58     6   3053   880     32
-Jeff Reed           165   39     2   13   9    16     3    196    44      2
-Jim Rice            618  200    20   98 110    62    13   7127  2163    351
-Jerry Royster       257   66     5   31  26    32    14   3910   979     33
-John Russell        315   76    13   35  60    25     3    630   151     24
-Juan Samuel         591  157    16   90  78    26     4   2020   541     52
-John Shelby         404   92    11   54  49    18     6   1354   325     30
-Joel Skinner        315   73     5   23  37    16     4    450   108      6
-Jeff Stone          249   69     6   32  19    20     4    702   209     10
-Jim Sundberg        429   91    12   41  42    57    13   5590  1397     83
-Jim Traber          212   54    13   28  44    18     2    233    59     13
-Jose Uribe          453  101     3   46  43    61     3    948   218      6
-Jerry Willard       161   43     4   17  26    22     3    707   179     21
-Joel Youngblood     184   47     5   20  28    18    11   3327   890     74
-Kevin Bass          591  184    20   83  79    38     5   1689   462     40
-Kal Daniels         181   58     6   34  23    22     1    181    58      6
-Kirk Gibson         441  118    28   84  86    68     8   2723   750    126
-Ken Griffey         490  150    21   69  58    35    14   6126  1839    121
-Keith Hernandez     551  171    13   94  83    94    13   6090  1840    128
-Kent Hrbek          550  147    29   85  91    71     6   2816   815    117
-Ken Landreaux       283   74     4   34  29    22    10   3919  1062     85
-Kevin McReynolds    560  161    26   89  96    66     4   1789   470     65
-Kevin Mitchell      328   91    12   51  43    33     2    342    94     12
-Keith Moreland      586  159    12   72  79    53     9   3082   880     83
-Ken Oberkfell       503  136     5   62  48    83    10   3423   970     20
-Ken Phelps          344   85    24   69  64    88     7    911   214     64
-Kirby Puckett       680  223    31  119  96    34     3   1928   587     35
-Kurt Stillwell      279   64     0   31  26    30     1    279    64      0
-Leon Durham         484  127    20   66  65    67     7   3006   844    116
-Len Dykstra         431  127     8   77  45    58     2    667   187      9
-Larry Herndon       283   70     8   33  37    27    12   4479  1222     94
-Lee Lacy            491  141    11   77  47    37    15   4291  1240     84
-Len Matuszek        199   52     9   26  28    21     6    805   191     30
-Lloyd Moseby        589  149    21   89  86    64     7   3558   928    102
-Lance Parrish       327   84    22   53  62    38    10   4273  1123    212
-Larry Parrish       464  128    28   67  94    52    13   5829  1552    210
-Luis Rivera         166   34     0   20  13    17     1    166    34      0
-Larry Sheets        338   92    18   42  60    21     3    682   185     36
-Lonnie Smith        508  146     8   80  44    46     9   3148   915     41
-Lou Whitaker        584  157    20   95  73    63    10   4704  1320     93
-Mike Aldrete        216   54     2   27  25    33     1    216    54      2
-Marty Barrett       625  179     4   94  60    65     5   1696   476     12
-Mike Brown          243   53     4   18  26    27     4    853   228     23
-Mike Davis          489  131    19   77  55    34     7   2051   549     62
-Mike Diaz           209   56    12   22  36    19     2    216    58     12
-Mariano Duncan      407   93     8   47  30    30     2    969   230     14
-Mike Easler         490  148    14   64  78    49    13   3400  1000    113
-Mike Fitzgerald     209   59     6   20  37    27     4    884   209     14
-Mel Hall            442  131    18   68  77    33     6   1416   398     47
-Mickey Hatcher      317   88     3   40  32    19     8   2543   715     28
-Mike Heath          288   65     8   30  36    27     9   2815   698     55
-Mike Kingery        209   54     3   25  14    12     1    209    54      3
-Mike LaValliere     303   71     3   18  30    36     3    344    76      3
-Mike Marshall       330   77    19   47  53    27     6   1928   516     90
-Mike Pagliarulo     504  120    28   71  71    54     3   1085   259     54
-Mark Salas          258   60     8   28  33    18     3    638   170     17
-Mike Schmidt         20    1     0    0   0     0     2     41     9      2
-Mike Scioscia       374   94     5   36  26    62     7   1968   519     26
-Mickey Tettleton    211   43    10   26  35    39     3    498   116     14
-Milt Thompson       299   75     6   38  23    26     3    580   160      8
-Mitch Webster       576  167     8   89  49    57     4    822   232     19
-Mookie Wilson       381  110     9   61  45    32     7   3015   834     40
-Marvell Wynne       288   76     7   34  37    15     4   1644   408     16
-Mike Young          369   93     9   43  42    49     5   1258   323     54
-Nick Esasky         330   76    12   35  41    47     4   1367   326     55
-Ozzie Guillen       547  137     2   58  47    12     2   1038   271      3
-Oddibe McDowell     572  152    18  105  49    65     2    978   249     36
-Omar Moreno         359   84     4   46  27    21    12   4992  1257     37
-Ozzie Smith         514  144     0   67  54    79     9   4739  1169     13
-Ozzie Virgil        359   80    15   45  48    63     7   1493   359     61
-Phil Bradley        526  163    12   88  50    77     4   1556   470     38
-Phil Garner         313   83     9   43  41    30    14   5885  1543    104
-Pete Incaviglia     540  135    30   82  88    55     1    540   135     30
-Paul Molitor        437  123     9   62  55    40     9   4139  1203     79
-Pete O'Brien        551  160    23   86  90    87     5   2235   602     75
-Pete Rose           237   52     0   15  25    30    24  14053  4256    160
-Pat Sheridan        236   56     6   41  19    21     5   1257   329     24
-Pat Tabler          473  154     6   61  48    29     6   1966   566     29
-Rafael Belliard     309   72     0   33  31    26     5    354    82      0
-Rick Burleson       271   77     5   35  29    33    12   4933  1358     48
-Randy Bush          357   96     7   50  45    39     5   1394   344     43
-Rick Cerone         216   56     4   22  18    15    12   2796   665     43
-Ron Cey             256   70    13   42  36    44    16   7058  1845    312
-Rob Deer            466  108    33   75  86    72     3    652   142     44
-Rick Dempsey        327   68    13   42  29    45    18   3949   939     78
-Rich Gedman         462  119    16   49  65    37     7   2131   583     69
-Ron Hassey          341  110     9   45  49    46     9   2331   658     50
-Rickey Henderson    608  160    28  130  74    89     8   4071  1182    103
-Reggie Jackson      419  101    18   65  58    92    20   9528  2510    548
-Ricky Jones          33    6     0    2   4     7     1     33     6      0
-Ron Kittle          376   82    21   42  60    35     5   1770   408    115
-Ray Knight          486  145    11   51  76    40    11   3967  1102     67
-Randy Kutcher       186   44     7   28  16    11     1    186    44      7
-Rudy Law            307   80     1   42  36    29     7   2421   656     18
-Rick Leach          246   76     5   35  39    13     6    912   234     12
-Rick Manning        205   52     8   31  27    17    12   5134  1323     56
-Rance Mulliniks     348   90    11   50  45    43    10   2288   614     43
-Ron Oester          523  135     8   52  44    52     9   3368   895     39
-Rey Quinones        312   68     2   32  22    24     1    312    68      2
-Rafael Ramirez      496  119     8   57  33    21     7   3358   882     36
-Ronn Reynolds       126   27     3    8  10     5     4    239    49      3
-Ron Roenicke        275   68     5   42  42    61     6    961   238     16
-Ryne Sandberg       627  178    14   68  76    46     6   3146   902     74
-Rafael Santana      394   86     1   38  28    36     4   1089   267      3
-Rick Schu           208   57     8   32  25    18     3    653   170     17
-Ruben Sierra        382  101    16   50  55    22     1    382   101     16
-Roy Smalley         459  113    20   59  57    68    12   5348  1369    155
-Robby Thompson      549  149     7   73  47    42     1    549   149      7
-Rob Wilfong         288   63     3   25  33    16    10   2682   667     38
-Reggie Williams     303   84     4   35  32    23     2    312    87      4
-Robin Yount         522  163     9   82  46    62    13   7037  2019    153
-Steve Balboni       512  117    29   54  88    43     6   1750   412    100
-Scott Bradley       220   66     5   20  28    13     3    290    80      5
-Sid Bream           522  140    16   73  77    60     4    730   185     22
-Steve Buechele      461  112    18   54  54    35     2    680   160     24
-Shawon Dunston      581  145    17   66  68    21     2    831   210     21
-Scott Fletcher      530  159     3   82  50    47     6   1619   426     11
-Steve Garvey        557  142    21   58  81    23    18   8759  2583    271
-Steve Jeltz         439   96     0   44  36    65     4    711   148      1
-Steve Lombardozzi   453  103     8   53  33    52     2    507   123      8
-Spike Owen          528  122     1   67  45    51     4   1716   403     12
-Steve Sax           633  210     6   91  56    59     6   3070   872     19
-Tony Armas           16    2     0    1   0     0     2     28     4      0
-Tony Bernazard      562  169    17   88  73    53     8   3181   841     61
-Tom Brookens        281   76     3   42  25    20     8   2658   657     48
-Tom Brunansky       593  152    23   69  75    53     6   2765   686    133
-Tony Fernandez      687  213    10   91  65    27     4   1518   448     15
-Tim Flannery        368  103     3   48  28    54     8   1897   493      9
-Tom Foley           263   70     1   26  23    30     4    888   220      9
-Tony Gwynn          642  211    14  107  59    52     5   2364   770     27
-Terry Harper        265   68     8   26  30    29     7   1337   339     32
-Toby Harrah         289   63     7   36  41    44    17   7402  1954    195
-Tommy Herr          559  141     2   48  61    73     8   3162   874     16
-Tim Hulett          520  120    17   53  44    21     4    927   227     22
-Terry Kennedy        19    4     1    2   3     1     1     19     4      1
-Tito Landrum        205   43     2   24  17    20     7    854   219     12
-Tim Laudner         193   47    10   21  29    24     6   1136   256     42
-Tom O'Malley        181   46     1   19  18    17     5    937   238      9
-Tom Paciorek        213   61     4   17  22     3    17   4061  1145     83
-Tony Pena           510  147    10   56  52    53     7   2872   821     63
-Terry Pendleton     578  138     1   56  59    34     3   1399   357      7
-Tony Perez          200   51     2   14  29    25    23   9778  2732    379
-Tony Phillips       441  113     5   76  52    76     5   1546   397     17
-Terry Puhl          172   42     3   17  14    15    10   4086  1150     57
-Tim Raines          580  194     9   91  62    78     8   3372  1028     48
-Ted Simmons         127   32     4   14  25    12    19   8396  2402    242
-Tim Teufel          279   69     4   35  31    32     4   1359   355     31
-Tim Wallach         480  112    18   50  71    44     7   3031   771    110
-Vince Coleman       600  139     0   94  29    60     2   1236   309      1
-Von Hayes           610  186    19  107  98    74     6   2728   753     69
-Vance Law           360   81     5   37  44    37     7   2268   566     41
-Wally Backman       387  124     1   67  27    36     7   1775   506      6
-Wade Boggs          580  207     8  107  71   105     5   2778   978     32
-Will Clark          408  117    11   66  41    34     1    408   117     11
-Wally Joyner        593  172    22   82 100    57     1    593   172     22
-Wayne Krenchicki    221   53     2   21  23    22     8   1063   283     15
-Willie McGee        497  127     7   65  48    37     5   2703   806     32
-Willie Randolph     492  136     5   76  50    94    12   5511  1511     39
-Wayne Tolleson      475  126     3   61  43    52     6   1700   433      7
-Willie Upshaw       573  144     9   85  60    78     8   3198   857     97
-Willie Wilson       631  170     9   77  44    31    11   4908  1457     30
                   CRuns CRBI CWalks League Division PutOuts Assists Errors
-Andy Allanson        30   29     14      A        E     446      33     20
-Alan Ashby          321  414    375      N        W     632      43     10
-Alvin Davis         224  266    263      A        W     880      82     14
-Andre Dawson        828  838    354      N        E     200      11      3
-Andres Galarraga     48   46     33      N        E     805      40      4
-Alfredo Griffin     501  336    194      A        W     282     421     25
-Al Newman            30    9     24      N        E      76     127      7
-Argenis Salazar      41   37     12      A        W     121     283      9
-Andres Thomas        32   34      8      N        W     143     290     19
-Andre Thornton      784  890    866      A        E       0       0      0
-Alan Trammell       702  504    488      A        E     238     445     22
-Alex Trevino        192  186    161      N        W     304      45     11
-Andy VanSlyke       205  204    203      N        E     211      11      7
-Alan Wiggins        309  103    207      A        E     121     151      6
-Bill Almon          376  290    238      N        E      80      45      8
-Billy Beane          20   16     11      A        W     118       0      0
-Buddy Bell         1045  993    732      N        W     105     290     10
-Buddy Biancalana     65   23     39      A        W     102     177     16
-Bruce Bochte        643  658    653      A        W     912      88      9
-Bruce Bochy          67   82     56      N        W     202      22      2
-Barry Bonds          72   48     65      N        E     280       9      5
-Bobby Bonilla        55   43     62      A        W     361      22      2
-Bob Boone             9    9      3      A        W     812      84     11
-Bob Brenly          242  251    240      N        W     518      55      3
-Bill Buckner       1008 1072    402      A        E    1067     157     14
-Brett Butler        442  198    317      A        E     434       9      3
-Bob Dernier         291  108    180      N        E     222       3      3
-Bo Diaz             246  327    166      N        W     732      83     13
-Bill Doran          349  182    308      N        W     262     329     16
-Brian Downing       763  734    784      A        W     267       5      3
-Bobby Grich        1033  864   1087      A        W     127     221      7
-Billy Hatcher        80   46     31      N        W     226       7      4
-Bob Horner          545  652    337      N        W    1378     102      8
-Brook Jacoby        219  208    136      A        E     109     292     25
-Bob Kearney         126  132     66      A        W     419      46      5
-Bill Madlock        859  803    571      N        W      72     170     24
-Bobby Meacham       156   86    107      A        E      70     149     12
-Bob Melvin           34   29     18      N        W     442      59      6
-Ben Oglivie         784  901    560      A        E       0       0      0
-Bip Roberts          34   12     14      N        W     166     172     10
-BillyJo Robidoux     20   29     45      A        E     326      29      5
-Bill Russell        796  627    483      N        W     103      84      5
-Billy Sample        371  230    195      N        W      69       1      1
-Bill Schroeder       86   76     32      A        E     307      25      1
-Butch Wynegar       486  493    608      A        E     325      22      2
-Chris Bando         108  117    118      A        E     359      30      4
-Chris Brown         113  121     80      N        W      73     177     18
-Carmen Castillo     117  107     51      A        E      58       4      4
-Cecil Cooper        987 1089    431      A        E     697      61      9
-Chili Davis         352  342    289      N        W     303       9      9
-Carlton Fisk       1003  977    619      A        W     389      39      4
-Curt Ford            32   32     27      N        E     109       7      3
-Cliff Johnson         3    4      4      A        E       0       0      0
-Carney Lansford     634  563    319      A        W      67     147      4
-Chet Lemon          747  666    526      A        E     316       6      5
-Candy Maldonado      99  138     64      N        W     161      10      3
-Carmelo Martinez    164  179    194      N        W     142      14      2
-Charlie Moore       441  401    333      A        E     425      43      4
-Craig Reynolds      409  321    170      N        W     106     206      7
-Cal Ripken          529  472    313      A        E     240     482     13
-Cory Snyder          58   69     16      A        E     203      70     10
-Chris Speier        698  661    777      N        E      53      88      3
-Curt Wilkerson      116   64     57      A        W     125     199     13
-Dave Anderson       118   69    114      N        W      73     152     11
-Doug Baker           20   12      9      A        W      80       4      0
-Don Baylor         1141 1179    727      A        E       0       0      0
-Dann Bilardello      61   74     52      N        E     391      38      8
-Daryl Boston         57   40     39      A        W     152       3      5
-Darnell Coles        99  103     78      A        E     107     242     23
-Dave Collins        612  344    422      A        E     211       2      1
-Dave Concepcion     950  909    690      N        W     153     223     10
-Darren Daulton       33   32     55      N        E     244      21      4
-Doug DeCinces       712  815    548      A        W     119     216     12
-Darrell Evans      1175 1152   1380      A        E     808     108      2
-Dwight Evans       1082  949    989      A        E     280      10      5
-Damaso Garcia       461  301    112      A        E     224     286      8
-Dan Gladden         196  110    117      N        W     226       7      3
-Danny Heep          144  149    153      N        E      83       2      1
-Dave Henderson      285  274    186      A        W     182       9      4
-Donnie Hill         123  108     55      A        W     104     213      9
-Dave Kingman        901 1210    608      A        W     463      32      8
-Davey Lopes        1019  608    820      N        E      51      54      8
-Don Mattingly       349  401    171      A        E    1377     100      6
-Darryl Motley       156  158     67      A        W      92       2      2
-Dale Murphy         813  822    617      N        W     303       6      6
-Dwayne Murphy       575  528    635      A        W     276       6      2
-Dave Parker         978 1093    495      N        W     278       9      9
-Dan Pasqua           61   70     63      A        E     148       4      2
-Darrell Porter      746  805    875      A        W     165       9      1
-Dick Schofield      160  123    122      A        W     246     389     18
-Don Slaught         156  159     76      A        W     533      40      4
-Darryl Strawberry   292  343    267      N        E     226      10      6
-Dale Sveum           35   35     32      A        E      45     122     26
-Danny Tartabull      87  110     71      A        W     157       7      8
-Dickie Thon         258  192    162      N        W     142     210     10
-Denny Walling       287  294    227      N        W      59     156      9
-Dave Winfield      1135 1234    791      A        E     292       9      5
-Enos Cabell         753  596    259      N        W     360      32      5
-Eric Davis          156  119     99      N        W     274       2      7
-Eddie Milner        335  174    258      N        W     292       6      3
-Eddie Murray        884 1015    709      A        E    1045      88     13
-Ernest Riles        123   92     90      A        E     212     327     20
-Ed Romero           166  122    106      A        E     102     132     10
-Ernie Whitt         266  323    248      A        E     709      41      7
-Fred Lynn           906  926    716      A        E     244       2      4
-Floyd Rayford       107  114     53      A        E      40     115     15
-Franklin Stubbs      77   77     61      N        W     206      10      7
-Frank White         743  693    300      A        W     316     439     10
-George Bell         297  319    117      A        E     269      17     10
-Glenn Braggs         19   18     11      A        E     116       5     12
-George Brett       1072 1050    695      A        W      97     218     16
-Greg Brock          195  219    214      N        W     726      87      3
-Gary Carter         847  999    680      N        E     869      62      8
-Glenn Davis         148  173     95      N        W    1253     111     11
-George Foster       986 1239    666      N        E      96       4      4
-Gary Gaetti         361  401    224      A        W     118     334     21
-Greg Gagne          102   80     50      A        W     228     377     26
-George Hendrick     915 1067    546      A        W     144       6      5
-Glenn Hubbard       429  365    410      N        W     282     487     19
-Garth Iorg          216  208     93      A        E      91     185     12
-Gary Matthews      1070  955    921      N        E     137       5      9
-Graig Nettles      1172 1267   1057      N        W      83     174     16
-Gary Pettis         247  126    198      A        W     462       9      7
-Gary Redus          284  141    219      N        E     185       8      4
-Garry Templeton     703  519    256      N        W     207     358     20
-Gorman Thomas       681  782    697      A        W       0       0      0
-Greg Walker         211  280    138      A        W     670      57      5
-Gary Ward           444  419    240      A        W     237       8      1
-Glenn Wilson        265  316    134      N        E     331      20      4
-Harold Baines       492  589    263      A        W     295      15      5
-Hubie Brooks        313  377    187      N        E     116     222     15
-Howard Johnson      145  154    128      N        E      50     136     20
-Hal McRae           935 1088    643      A        W       0       0      0
-Harold Reynolds      72   31     48      A        W     278     415     16
-Harry Spilman        80   97     61      N        W     138      15      1
-Herm Winningham      58   37     47      N        E      97       2      2
-Jesse Barfield      371  376    238      A        E     368      20      3
-Juan Beniquez       581  421    325      A        E     211      56     13
-Juan Bonilla        139   98    111      A        E     122     140      5
-John Cangelosi       67   32     71      A        W     276       7      9
-Jose Canseco        101  130     69      A        W     319       4     14
-Joe Carter          210  222     68      A        E     241       8      6
-Jack Clark          702  705    625      N        E     623      35      3
-Jose Cruz           980 1032    854      N        W     237       5      4
-Julio Cruz          557  279    478      A        W     132     205      5
-Jody Davis          273  383    226      N        E     885     105      8
-Jim Dwyer           304  268    298      A        E      33       3      0
-Julio Franco        330  326    158      A        E     231     374     18
-Jim Gantner         450  367    241      A        E     304     347     10
-Johnny Grubb        544  462    551      A        E       0       0      0
-Jerry Hairston      202  185    257      A        W     132       9      0
-Jack Howell          45   39     35      A        W      28      56      2
-John Kruk            33   38     45      N        W     102       4      2
-Jeffrey Leonard     379  428    221      N        W     158       4      5
-Jim Morrison        302  351    174      N        E      92     257     20
-John Moses           89   48     54      A        W     211       9      3
-Jerry Mumphrey      616  522    436      N        E     161       3      3
-Joe Orsulak         126   44     55      N        E     193      11      4
-Jorge Orta          730  741    497      A        W       0       0      0
-Jim Presley         181  227     82      A        W     110     308     15
-Jamie Quirk         100  125     63      A        W     260      58      4
-Johnny Ray          366  337    218      N        E     280     479      5
-Jeff Reed            18   10     18      A        W     332      19      2
-Jim Rice           1104 1289    564      A        E     330      16      8
-Jerry Royster       518  324    382      N        W      87     166     14
-John Russell         68   94     55      N        E     498      39     13
-Juan Samuel         310  226     91      N        E     290     440     25
-John Shelby         188  135     63      A        E     222       5      5
-Joel Skinner         38   46     28      A        W     227      15      3
-Jeff Stone           97   48     44      N        E     103       8      2
-Jim Sundberg        578  579    644      A        W     686      46      4
-Jim Traber           31   46     20      A        E     243      23      5
-Jose Uribe           96   72     91      N        W     249     444     16
-Jerry Willard        77   99     76      A        W     300      12      2
-Joel Youngblood     419  382    304      N        W      49       2      0
-Kevin Bass          219  195     82      N        W     303      12      5
-Kal Daniels          34   23     22      N        W      88       0      3
-Kirk Gibson         433  420    309      A        E     190       2      2
-Ken Griffey         983  707    600      A        E      96       5      3
-Keith Hernandez     969  900    917      N        E    1199     149      5
-Kent Hrbek          405  474    319      A        W    1218     104     10
-Ken Landreaux       505  456    283      N        W     145       5      7
-Kevin McReynolds    233  260    155      N        W     332       9      8
-Kevin Mitchell       51   44     33      N        E     145      59      8
-Keith Moreland      363  477    295      N        E     181      13      4
-Ken Oberkfell       408  303    414      N        W      65     258      8
-Ken Phelps          150  156    187      A        W       0       0      0
-Kirby Puckett       262  201     91      A        W     429       8      6
-Kurt Stillwell       31   26     30      N        W     107     205     16
-Leon Durham         436  458    377      N        E    1231      80      7
-Len Dykstra         117   64     88      N        E     283       8      3
-Larry Herndon       557  483    307      A        E     156       2      2
-Lee Lacy            615  430    340      A        E     239       8      2
-Len Matuszek        113  119     87      N        W     235      22      5
-Lloyd Moseby        513  471    351      A        E     371       6      6
-Lance Parrish       577  700    334      A        E     483      48      6
-Larry Parrish       740  840    452      A        W       0       0      0
-Luis Rivera          20   13     17      N        E      64     119      9
-Larry Sheets         88  112     50      A        E       0       0      0
-Lonnie Smith        571  289    326      A        W     245       5      9
-Lou Whitaker        724  522    576      A        E     276     421     11
-Mike Aldrete         27   25     33      N        W     317      36      1
-Marty Barrett       216  163    166      A        E     303     450     14
-Mike Brown          101  110     76      N        E     107       3      3
-Mike Davis          300  263    153      A        W     310       9      9
-Mike Diaz            24   37     19      N        E     201       6      3
-Mariano Duncan      121   69     68      N        W     172     317     25
-Mike Easler         445  491    301      A        E       0       0      0
-Mike Fitzgerald      66  106     92      N        E     415      35      3
-Mel Hall            210  203    136      A        E     233       7      7
-Mickey Hatcher      269  270    118      A        W     220      16      4
-Mike Heath          315  325    189      N        E     259      30     10
-Mike Kingery         25   14     12      A        W     102       6      3
-Mike LaValliere      20   36     45      N        E     468      47      6
-Mike Marshall       247  288    161      N        W     149       8      6
-Mike Pagliarulo     150  167    114      A        E     103     283     19
-Mark Salas           80   75     36      A        W     358      32      8
-Mike Schmidt          6    7      4      N        E      78     220      6
-Mike Scioscia       181  199    288      N        W     756      64     15
-Mickey Tettleton     59   55     78      A        W     463      32      8
-Milt Thompson        71   33     44      N        E     212       1      2
-Mitch Webster       132   83     79      N        E     325      12      8
-Mookie Wilson       451  249    168      N        E     228       7      5
-Marvell Wynne       198  120    113      N        W     203       3      3
-Mike Young          181  177    157      A        E     149       1      6
-Nick Esasky         167  198    167      N        W     512      30      5
-Ozzie Guillen       129   80     24      A        W     261     459     22
-Oddibe McDowell     168   91    101      A        W     325      13      3
-Omar Moreno         699  386    387      N        W     151       8      5
-Ozzie Smith         583  374    528      N        E     229     453     15
-Ozzie Virgil        176  202    175      N        W     682      93     13
-Phil Bradley        245  167    174      A        W     250      11      1
-Phil Garner         751  714    535      N        W      58     141     23
-Pete Incaviglia      82   88     55      A        W     157       6     14
-Paul Molitor        676  390    364      A        E      82     170     15
-Pete O'Brien        278  328    273      A        W    1224     115     11
-Pete Rose          2165 1314   1566      N        W     523      43      6
-Pat Sheridan        166  125    105      A        E     172       1      4
-Pat Tabler          250  252    178      A        E     846      84      9
-Rafael Belliard      41   32     26      N        E     117     269     12
-Rick Burleson       630  435    403      A        W      62      90      3
-Randy Bush          178  192    136      A        W     167       2      4
-Rick Cerone         266  304    198      A        E     391      44      4
-Ron Cey             965 1128    990      N        E      41     118      8
-Rob Deer            102  109    102      A        E     286       8      8
-Rick Dempsey        438  380    466      A        E     659      53      7
-Rich Gedman         244  288    150      A        E     866      65      6
-Ron Hassey          249  322    274      A        E     251       9      4
-Rickey Henderson    862  417    708      A        E     426       4      6
-Reggie Jackson     1509 1659   1342      A        W       0       0      0
-Ricky Jones           2    4      7      A        W     205       5      4
-Ron Kittle          238  299    157      A        W       0       0      0
-Ray Knight          410  497    284      N        E      88     204     16
-Randy Kutcher        28   16     11      N        W      99       3      1
-Rudy Law            379  198    184      A        W     145       2      2
-Rick Leach          102   96     80      A        E      44       0      1
-Rick Manning        643  445    459      A        E     155       3      2
-Rance Mulliniks     295  273    269      A        E      60     176      6
-Ron Oester          377  284    296      N        W     367     475     19
-Rey Quinones         32   22     24      A        E      86     150     15
-Rafael Ramirez      365  280    165      N        W     155     371     29
-Ronn Reynolds        16   13     14      N        E     190       2      9
-Ron Roenicke        128  104    172      N        E     181       3      2
-Ryne Sandberg       494  345    242      N        E     309     492      5
-Rafael Santana       94   71     76      N        E     203     369     16
-Rick Schu            98   54     62      N        E      42      94     13
-Ruben Sierra         50   55     22      A        W     200       7      6
-Roy Smalley         713  660    735      A        W       0       0      0
-Robby Thompson       73   47     42      N        W     255     450     17
-Rob Wilfong         315  259    204      A        W     135     257      7
-Reggie Williams      39   32     23      N        W     179       5      3
-Robin Yount        1043  827    535      A        E     352       9      1
-Steve Balboni       204  276    155      A        W    1236      98     18
-Scott Bradley        27   31     15      A        W     281      21      3
-Sid Bream            93  106     86      N        E    1320     166     17
-Steve Buechele       76   75     49      A        W     111     226     11
-Shawon Dunston      106   86     40      N        E     320     465     32
-Scott Fletcher      218  149    163      A        W     196     354     15
-Steve Garvey       1138 1299    478      N        W    1160      53      7
-Steve Jeltz          68   56     99      N        E     229     406     22
-Steve Lombardozzi    63   39     58      A        W     289     407      6
-Spike Owen          211  146    155      A        W     209     372     17
-Steve Sax           420  230    274      N        W     367     432     16
-Tony Armas            1    0      0      A        E     247       4      8
-Tony Bernazard      450  342    373      A        E     351     442     17
-Tom Brookens        324  300    179      A        E     106     144      7
-Tom Brunansky       369  384    321      A        W     315      10      6
-Tony Fernandez      196  137     89      A        E     294     445     13
-Tim Flannery        207  162    198      N        W     209     246      3
-Tom Foley            83   82     86      N        E      81     147      4
-Tony Gwynn          352  230    193      N        W     337      19      4
-Terry Harper        135  163    128      N        W      92       5      3
-Toby Harrah        1115  919   1153      A        W     166     211      7
-Tommy Herr          421  349    359      N        E     352     414      9
-Tim Hulett          106   80     52      A        W      70     144     11
-Terry Kennedy         2    3      1      N        W     692      70      8
-Tito Landrum        105   99     71      N        E     131       6      1
-Tim Laudner         129  139    106      A        W     299      13      5
-Tom O'Malley         88   95    104      A        E      37      98      9
-Tom Paciorek        488  491    244      A        W     178      45      4
-Tony Pena           307  340    174      N        E     810      99     18
-Terry Pendleton     149  161     87      N        E     133     371     20
-Tony Perez         1272 1652    925      N        W     398      29      7
-Tony Phillips       226  149    191      A        W     160     290     11
-Terry Puhl          579  363    406      N        W      65       0      0
-Tim Raines          604  314    469      N        E     270      13      6
-Ted Simmons        1048 1348    819      N        W     167      18      6
-Tim Teufel          180  148    158      N        E     133     173      9
-Tim Wallach         338  406    239      N        E      94     270     16
-Vince Coleman       201   69    110      N        E     300      12      9
-Von Hayes           399  366    286      N        E    1182      96     13
-Vance Law           279  257    246      N        E     170     284      3
-Wally Backman       272  125    194      N        E     186     290     17
-Wade Boggs          474  322    417      A        E     121     267     19
-Will Clark           66   41     34      N        W     942      72     11
-Wally Joyner         82  100     57      A        W    1222     139     15
-Wayne Krenchicki    107  124    106      N        E     325      58      6
-Willie McGee        379  311    138      N        E     325       9      3
-Willie Randolph     897  451    875      A        E     313     381     20
-Wayne Tolleson      217   93    146      A        W      37     113      7
-Willie Upshaw       470  420    332      A        E    1314     131     12
-Willie Wilson       775  357    249      A        W     408       4      3
                     Salary NewLeague
-Andy Allanson           NA         A
-Alan Ashby         475.000         N
-Alvin Davis        480.000         A
-Andre Dawson       500.000         N
-Andres Galarraga    91.500         N
-Alfredo Griffin    750.000         A
-Al Newman           70.000         A
-Argenis Salazar    100.000         A
-Andres Thomas       75.000         N
-Andre Thornton    1100.000         A
-Alan Trammell      517.143         A
-Alex Trevino       512.500         N
-Andy VanSlyke      550.000         N
-Alan Wiggins       700.000         A
-Bill Almon         240.000         N
-Billy Beane             NA         A
-Buddy Bell         775.000         N
-Buddy Biancalana   175.000         A
-Bruce Bochte            NA         A
-Bruce Bochy        135.000         N
-Barry Bonds        100.000         N
-Bobby Bonilla      115.000         N
-Bob Boone               NA         A
-Bob Brenly         600.000         N
-Bill Buckner       776.667         A
-Brett Butler       765.000         A
-Bob Dernier        708.333         N
-Bo Diaz            750.000         N
-Bill Doran         625.000         N
-Brian Downing      900.000         A
-Bobby Grich             NA         A
-Billy Hatcher      110.000         N
-Bob Horner              NA         N
-Brook Jacoby       612.500         A
-Bob Kearney        300.000         A
-Bill Madlock       850.000         N
-Bobby Meacham           NA         A
-Bob Melvin          90.000         N
-Ben Oglivie             NA         A
-Bip Roberts             NA         N
-BillyJo Robidoux    67.500         A
-Bill Russell            NA         N
-Billy Sample            NA         N
-Bill Schroeder     180.000         A
-Butch Wynegar           NA         A
-Chris Bando        305.000         A
-Chris Brown        215.000         N
-Carmen Castillo    247.500         A
-Cecil Cooper            NA         A
-Chili Davis        815.000         N
-Carlton Fisk       875.000         A
-Curt Ford           70.000         N
-Cliff Johnson           NA         A
-Carney Lansford   1200.000         A
-Chet Lemon         675.000         A
-Candy Maldonado    415.000         N
-Carmelo Martinez   340.000         N
-Charlie Moore           NA         A
-Craig Reynolds     416.667         N
-Cal Ripken        1350.000         A
-Cory Snyder         90.000         A
-Chris Speier       275.000         N
-Curt Wilkerson     230.000         A
-Dave Anderson      225.000         N
-Doug Baker              NA         A
-Don Baylor         950.000         A
-Dann Bilardello         NA         N
-Daryl Boston        75.000         A
-Darnell Coles      105.000         A
-Dave Collins            NA         A
-Dave Concepcion    320.000         N
-Darren Daulton          NA         N
-Doug DeCinces      850.000         A
-Darrell Evans      535.000         A
-Dwight Evans       933.333         A
-Damaso Garcia      850.000         N
-Dan Gladden        210.000         A
-Danny Heep              NA         N
-Dave Henderson     325.000         A
-Donnie Hill        275.000         A
-Dave Kingman            NA         A
-Davey Lopes        450.000         N
-Don Mattingly     1975.000         A
-Darryl Motley           NA         A
-Dale Murphy       1900.000         N
-Dwayne Murphy      600.000         A
-Dave Parker       1041.667         N
-Dan Pasqua         110.000         A
-Darrell Porter     260.000         A
-Dick Schofield     475.000         A
-Don Slaught        431.500         A
-Darryl Strawberry 1220.000         N
-Dale Sveum          70.000         A
-Danny Tartabull    145.000         A
-Dickie Thon             NA         N
-Denny Walling      595.000         N
-Dave Winfield     1861.460         A
-Enos Cabell             NA         N
-Eric Davis         300.000         N
-Eddie Milner       490.000         N
-Eddie Murray      2460.000         A
-Ernest Riles            NA         A
-Ed Romero          375.000         A
-Ernie Whitt             NA         A
-Fred Lynn               NA         A
-Floyd Rayford           NA         A
-Franklin Stubbs         NA         N
-Frank White        750.000         A
-George Bell       1175.000         A
-Glenn Braggs        70.000         A
-George Brett      1500.000         A
-Greg Brock         385.000         A
-Gary Carter       1925.571         N
-Glenn Davis        215.000         N
-George Foster           NA         N
-Gary Gaetti        900.000         A
-Greg Gagne         155.000         A
-George Hendrick    700.000         A
-Glenn Hubbard      535.000         N
-Garth Iorg         362.500         A
-Gary Matthews      733.333         N
-Graig Nettles      200.000         N
-Gary Pettis        400.000         A
-Gary Redus         400.000         A
-Garry Templeton    737.500         N
-Gorman Thomas           NA         A
-Greg Walker        500.000         A
-Gary Ward          600.000         A
-Glenn Wilson       662.500         N
-Harold Baines      950.000         A
-Hubie Brooks       750.000         N
-Howard Johnson     297.500         N
-Hal McRae          325.000         A
-Harold Reynolds     87.500         A
-Harry Spilman      175.000         N
-Herm Winningham     90.000         N
-Jesse Barfield    1237.500         A
-Juan Beniquez      430.000         A
-Juan Bonilla            NA         N
-John Cangelosi     100.000         N
-Jose Canseco       165.000         A
-Joe Carter         250.000         A
-Jack Clark        1300.000         N
-Jose Cruz          773.333         N
-Julio Cruz              NA         A
-Jody Davis        1008.333         N
-Jim Dwyer          275.000         A
-Julio Franco       775.000         A
-Jim Gantner        850.000         A
-Johnny Grubb       365.000         A
-Jerry Hairston          NA         A
-Jack Howell         95.000         A
-John Kruk          110.000         N
-Jeffrey Leonard    100.000         N
-Jim Morrison       277.500         N
-John Moses          80.000         A
-Jerry Mumphrey     600.000         N
-Joe Orsulak             NA         N
-Jorge Orta              NA         A
-Jim Presley        200.000         A
-Jamie Quirk             NA         A
-Johnny Ray         657.000         N
-Jeff Reed           75.000         N
-Jim Rice          2412.500         A
-Jerry Royster      250.000         A
-John Russell       155.000         N
-Juan Samuel        640.000         N
-John Shelby        300.000         A
-Joel Skinner       110.000         A
-Jeff Stone              NA         N
-Jim Sundberg       825.000         N
-Jim Traber              NA         A
-Jose Uribe         195.000         N
-Jerry Willard           NA         A
-Joel Youngblood    450.000         N
-Kevin Bass         630.000         N
-Kal Daniels         86.500         N
-Kirk Gibson       1300.000         A
-Ken Griffey       1000.000         N
-Keith Hernandez   1800.000         N
-Kent Hrbek        1310.000         A
-Ken Landreaux      737.500         N
-Kevin McReynolds   625.000         N
-Kevin Mitchell     125.000         N
-Keith Moreland    1043.333         N
-Ken Oberkfell      725.000         N
-Ken Phelps         300.000         A
-Kirby Puckett      365.000         A
-Kurt Stillwell      75.000         N
-Leon Durham       1183.333         N
-Len Dykstra        202.500         N
-Larry Herndon      225.000         A
-Lee Lacy           525.000         A
-Len Matuszek       265.000         N
-Lloyd Moseby       787.500         A
-Lance Parrish      800.000         N
-Larry Parrish      587.500         A
-Luis Rivera             NA         N
-Larry Sheets       145.000         A
-Lonnie Smith            NA         A
-Lou Whitaker       420.000         A
-Mike Aldrete        75.000         N
-Marty Barrett      575.000         A
-Mike Brown              NA         N
-Mike Davis         780.000         A
-Mike Diaz           90.000         N
-Mariano Duncan     150.000         N
-Mike Easler        700.000         N
-Mike Fitzgerald         NA         N
-Mel Hall           550.000         A
-Mickey Hatcher          NA         A
-Mike Heath         650.000         A
-Mike Kingery        68.000         A
-Mike LaValliere    100.000         N
-Mike Marshall      670.000         N
-Mike Pagliarulo    175.000         A
-Mark Salas         137.000         A
-Mike Schmidt      2127.333         N
-Mike Scioscia      875.000         N
-Mickey Tettleton   120.000         A
-Milt Thompson      140.000         N
-Mitch Webster      210.000         N
-Mookie Wilson      800.000         N
-Marvell Wynne      240.000         N
-Mike Young         350.000         A
-Nick Esasky             NA         N
-Ozzie Guillen      175.000         A
-Oddibe McDowell    200.000         A
-Omar Moreno             NA         N
-Ozzie Smith       1940.000         N
-Ozzie Virgil       700.000         N
-Phil Bradley       750.000         A
-Phil Garner        450.000         N
-Pete Incaviglia    172.000         A
-Paul Molitor      1260.000         A
-Pete O'Brien            NA         A
-Pete Rose          750.000         N
-Pat Sheridan       190.000         A
-Pat Tabler         580.000         A
-Rafael Belliard    130.000         N
-Rick Burleson      450.000         A
-Randy Bush         300.000         A
-Rick Cerone        250.000         A
-Ron Cey           1050.000         A
-Rob Deer           215.000         A
-Rick Dempsey       400.000         A
-Rich Gedman             NA         A
-Ron Hassey         560.000         A
-Rickey Henderson  1670.000         A
-Reggie Jackson     487.500         A
-Ricky Jones             NA         A
-Ron Kittle         425.000         A
-Ray Knight         500.000         A
-Randy Kutcher           NA         N
-Rudy Law                NA         A
-Rick Leach         250.000         A
-Rick Manning       400.000         A
-Rance Mulliniks    450.000         A
-Ron Oester         750.000         N
-Rey Quinones        70.000         A
-Rafael Ramirez     875.000         N
-Ronn Reynolds      190.000         N
-Ron Roenicke       191.000         N
-Ryne Sandberg      740.000         N
-Rafael Santana     250.000         N
-Rick Schu          140.000         N
-Ruben Sierra        97.500         A
-Roy Smalley        740.000         A
-Robby Thompson     140.000         N
-Rob Wilfong        341.667         A
-Reggie Williams         NA         N
-Robin Yount       1000.000         A
-Steve Balboni      100.000         A
-Scott Bradley       90.000         A
-Sid Bream          200.000         N
-Steve Buechele     135.000         A
-Shawon Dunston     155.000         N
-Scott Fletcher     475.000         A
-Steve Garvey      1450.000         N
-Steve Jeltz        150.000         N
-Steve Lombardozzi  105.000         A
-Spike Owen         350.000         A
-Steve Sax           90.000         N
-Tony Armas              NA         A
-Tony Bernazard     530.000         A
-Tom Brookens       341.667         A
-Tom Brunansky      940.000         A
-Tony Fernandez     350.000         A
-Tim Flannery       326.667         N
-Tom Foley          250.000         N
-Tony Gwynn         740.000         N
-Terry Harper       425.000         A
-Toby Harrah             NA         A
-Tommy Herr         925.000         N
-Tim Hulett         185.000         A
-Terry Kennedy      920.000         A
-Tito Landrum       286.667         N
-Tim Laudner        245.000         A
-Tom O'Malley            NA         A
-Tom Paciorek       235.000         A
-Tony Pena         1150.000         N
-Terry Pendleton    160.000         N
-Tony Perez              NA         N
-Tony Phillips      425.000         A
-Terry Puhl         900.000         N
-Tim Raines              NA         N
-Ted Simmons        500.000         N
-Tim Teufel         277.500         N
-Tim Wallach        750.000         N
-Vince Coleman      160.000         N
-Von Hayes         1300.000         N
-Vance Law          525.000         N
-Wally Backman      550.000         N
-Wade Boggs        1600.000         A
-Will Clark         120.000         N
-Wally Joyner       165.000         A
-Wayne Krenchicki        NA         N
-Willie McGee       700.000         N
-Willie Randolph    875.000         A
-Wayne Tolleson     385.000         A
-Willie Upshaw      960.000         A
-Willie Wilson     1000.000         A
  • Take a look at the variables in the data

Decision Trees - Regression

  • Task - You want to predict Salary of players from the number of Years they played and the number of Hits in the previous year
  • Can you write a regression equation for this?
  • Let us take a look at the plot
Hitters |>
ggplot(aes(x = Years, y = Hits)) +
  geom_point(aes(colour = Salary))

Decision Trees - Regression

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • You want to predict Salary (annual salary of player )from Years (Number of years in leagues) and Hits (Number of hits)
  • Look at the decision tree below

Source : ISLR : Chapter 8

Decision Trees

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • The first split in the tree is such that all observations where Years < 4.5 are in the left branch
  • The predicted salary for these players is given by the mean response of all observations in this split
  • For these observations, salary is log of 5.107 i.e. $165,174
  • All the observations where Years > 4.5 are on the other side, which are further split based on the number of hits in the previous season
  • Overall, the tree divides the data into 3 regions as - \[R_1 = (X | Years <4.5) , R_2 =(X | Years>=4.5, Hits<117.5), R3 = (X | Years>=4.5, Hits>=117.5)\]

Decision Trees - Terminologies

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • As like the tree analogy, the regions \[R_1, R_2, R_3\] are known as terminal nodes, just like leaves of the tree
  • The points along the tree where the predictor space is split are referred to as internal nodes
  • The lines that connect the tree to the nodes are the branches

Decision Trees - Regression

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • For better understanding, let us also look at a graph which shows how the regions are split
  • Why boxes? Simply because they are easier to interpret

Source : ISLR : Chapter 8

The process of building a decision trees

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • Simply put, two steps:
  • You have N (n1, n2, n3, n4 ….) predictors in the space into non-overlapping regions (R1, R2, R3…..Rj)
  • For each observation that we make for a region R1 , we assume that all the observations lying in that region have the same prediction, which is given by the mean of the all the values in that region

Decision Trees - Recursive Binary Splitting

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • The goal is to find boxes R1, . . . , Rj that minimize the RSS, given by

\[\sum_{j=1}^J \sum_{i \in Rj}{(y_i - \hat y_{Rj})}^2\] where \[\hat y_{Rj}\] is the mean response for the training observations within the jth box

Decision Trees - Recursive Binary Splitting

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • Since it is not computationally feasible to calculate this for each possible predictor, we use the top down, greedy approach
  • Also called the recursive binary splitting method
  • Named so because it begins at the start of the tree - at a point where all the observations belong to a single region
  • It then successively splits the predictor space such that each split is indicated via two new branches further down on the tree
  • Also named greedy approach because at each step, the best split is made at that particular step, rather than looking ahead and picking a split that will lead to a better tree in some future step

Decision Trees - Tree Pruning

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

  • The previous approach would overfit the data
  • An alternative approach is tree pruning
  • Grow a very large tree and then prune it in order to obtain a subtree
  • How can we decide the way to prune a tree?
  • This becomes a problem since there are infinite options to do so, given the large number of subtrees
  • Cost complexity pruning , also known as weakest link pruning provides a way
  • Rather than considering every possible subtree, we consider a sequence of trees indexed by a nonnegative tuning parameter α

Decision Trees - Tree Pruning

Content for this topic has been sourced from An Introduction to Statistical Learning. Please check out the work for detailed information.

\[\sum_{m=1}^{|T|} \sum_{x \in Rm}{(y_i - \hat y_{Rm})}^2 + \alpha * |T|\]

  • Number of terminal nodes of the tree T is denoted by |T|
  • Rm is the rectangle corresponding to the mth terminal node
  • \[\hat y_{Rm}\] is the predicted response associated with Rm (mean of the training observations in Rm)
  • The tuning parameter α controls a trade-off between the subtree’s complexity and its fit to the training data
  • As α increases, there is a price to pay for having a tree with many terminal nodes, and so there would be a smaller subtree

Decision Trees - Hitters Data

  • Making the decision tree
hitters_tree <- tree(Salary ~ . , Hitters)

plot(hitters_tree)
text(hitters_tree, pretty = 0)

Thank You :)